One can intersect a dodecahedron with a plane and obtain an equilateral triangle, a square, a regular pentagon, a regular hexagon, and a regular decagon:

_{(Image of 6- and 10-gon from Mathworld.)}

Q1. Does there exist a regular 7-gon, 8-gon, or 9-gon cross-section of the dodecahedron?

I can achieve, e.g., an irregular octagon, but not a regular octagon.

Q2. Can all five Platonic solids be achieved as cross-sections of one of the six regular 4-polytopes?

I haven't given this much thought, but the 120-cell seems the most likely candidate, as its facets are dodecahedra.